Given that a is a positive integer, show that
√3a(√12a + a√3a)
is always a multiple of 3.

Input note: write the expression in the form 3(...)

Answer:

[tex]117.8cm ^{2} [/tex]

Step-by-step explanation:

[tex]a = {r}^{2} \theta \: \div 2 \\ = 100 \times 135 \div 2 \\ = 117.8 \: {cm}^{2} [/tex]

Answer: B

Step-by-step explanation:

Range will always be Y

Domain will always be X

The equation of the lines is,

1. (4, -1); m = 3 : - y = 3x - 13

2. (-8, 0); m = -4 :- y = -4x - 24

3. (-6, -10); m = 1/6 :- y = -1/6x - 9

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The equation of the lines will be,

y = mx + c

y = 3x + c

-1 = 4 x 3 + c

c = -13

y = 3x - 13

y = mx + c

y = -4x + c

0 = -4 x -8 + c

c = -24

y = -x -24

y = mx + c

y = 1/6x + c

-10 = -1 + c

c = -9

y = -1/6x - 9

Therefore, the equation of the lines is,y = 3x - 13 y = -4x - 24 and y = -1/6x - 9.

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It will be 38 feet long

The perimeter is the space surrounding a shape's edge.

The sum of the lengths of all the sides in a rectangular shape is its perimeter. P = 2( L+B)

Given that a rectangle's width is 17 feet and its perimeter is 110 feet, the length will be P = 2 (L + B)

110 = 2 (L + 17)

55 - 17 = L.

The pool is therefore 38 feet long.

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Half a mile every hour is equal to 1/5 mile every 4/10th of an hour.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

(1/5) / (4/10) = x / 1

Cross-multiplication yielding

1/5 * 1 = 4/10 * x

How to find x?

10 / 20 = x

x = 1 / 2

Half a mile every hour is equal to 1/5 mile every 4/10th of an hour.

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Answer:

5 groups

Step-by-step explanation:

10/2=5

Out of the 14 coins she has, she will have 4 dimes, totaling $2.5.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a whole sentence.

Here,

Let n be the nickels, d be the dimes, q be the quarters.

Total coins=14

Total amount=$2.5

n=2d

d=2q

q=d/2

d+q+n=14

d+2d+d/2=14

2d+4d+d=28

7d=28

d=4

She will have 4 dimes out of 14 coins that she owns with an amount of $2.5.

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Answer:

1. no solution

2. one solution

3. infinitely many solutions

4. one solution

Step-by-step explanation:

1. same slope, different intercepts, parallel lines, no solution

2. different slopes, lines intersect at 1 point, one solution

3. same equation, infinitely many solutions

4. different slopes, lines intersect at 1 point, one solution

A graph of the given system of equations f(x) = 2x² - 8x + 3 and g(x) = -2x + 3 is shown in the image attached below.

The points that make both equations true is (0, 3)

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.

In Mathematics, the graph of every quadratic equations (functions) is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic equation (function) would always form a parabolic curve.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each, which is the ordered pair (0, 3);

f(x) = 2x² - 8x + 3

3 = 2(0)² - 8(0) + 3

3 = 3 (True).

g(x) = -2x + 3

3 = -2(0) + 3

3 = 3 (True).

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Answer:

Step-by-step explanation: One denominator in the question is 4/5 and another is 1/2. A common denominator would be /10 because it applies to /5 and /2.

The amount of simple interest is (a) $341.60

From the question, we have the following parameters that can be used in our computation:

Principal, P = $800

Rate, r = 6.1 %

Time = 7 years

The simple interest on the investment is calculated as

I = PRT

Substitute the known values in the above equation, so, we have the following representation

I = 800 * 6.1% * 7

Express 6.1% as decimal

So, we have the following representation

I = 800 * 0.061 * 7

Evaluate the products

I = 341.6

Hence, the amount is (a) $341.6

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Answer: To estimate the company's sales in 2026, we need to find the average increase in sales per year and then use that to predict the sales for 2026.

The total increase in sales from 2017 to 2020 was $14.5 million - $9 million = $<<14.5-9=5.5>>5.5 million.

The number of years from 2017 to 2020 is 2020 - 2017 = <<2020-2017=3>>3 years.

Therefore, the average increase in sales per year was $5.5 million / 3 years = $<<5.5/3=1.83>>1.83 million/year.

Since the average increase in sales per year was $1.83 million/year, we can estimate the sales in 2026 by adding that amount to the sales for each year from 2020 to 2026. For example, the estimated sales for 2021 would be $14.5 million + $1.83 million = $16.33 million. Similarly, the estimated sales for 2022 would be $16.33 million + $1.83 million = $18.16 million, and so on.

Using this method, we can estimate that the sales for 2026 will be $26.73 million.

The depth of the water is 5.3 meters

The dolphin jumps to a height of 4.5 over the water's surface, and her companion swims 9.8 straight beneath her, according to the story.

We will take the position of the dolphin's friend and subtract it from the dolphin's position to determine the location of the dolphin's friend with respect to the water's surface.

-5.3 denotes the depth of the water.

As a result, the friend of the dolphin is located 5.3 meters below the water's surface.

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Answer:

[tex]7\sqrt5[/tex]

Step-by-step explanation:

245 ÷ 5 = 49

49 is a square number (7)

So you put 7 on the outside and 5 on the inside.

On solving the provided question, we got that The 90% confidence interval for the population mean mu is (140.4, 147.6)

A measure of how far the data are from the mean is called standard deviation (or). Data that have a low standard deviation are more likely to be centered around the mean than those that have a high standard deviation.

xbar = 144 (sample mean)

s = 12 (sample standard deviation)

n = 30 (sample size)

z = 1.645 (critical value at 90% confidence; use a calculator or table to compute this value)

[tex]The lower limit of the confidence interval is L, which is found by\\\\L = xbar - z(s/sqrt(n))\\L = 144 - 1.645(12/sqrt(30))\\L = 140.395985571616\\L = 140.4\\[/tex]

Similarly the upper limit U is

U = xbar + z(s/sqrt(n))

U = 144 + 1.645(12/sqrt(30))

U = 147.604014428384

U = 147.6

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Answer:

0.004

Step-by-step explanation:

Hope it helps!

Answer:

It A

Step-by-step explanation:

Answer: I = $ 200.00

Step-by-step explanation:

I = Prt

Convert R (percent) to r (decimal)

r = R/100 = 1%/100 = 0.01 per year

I = 2000 × 0.01 × 10 = 200

I = $ 200.00

hope this helps!

Answer:

x = 4

Step-by-step explanation:

5 x .8 = 4

Answer: the value of x is 4

Step-by-step explanation:

x=5*0.8=4

After solving the given equation for c, we know that the value of c is (A) -56.

Equivalent systems refer to sets of equations with the same solution.

We can create an analogous system from a system of two equations by replacing one equation with the total of the two equations or by replacing an equation with a multiple of itself.

So, we have the equation:

-5 = 9+(c/4)

Now, solve for the subject c as follows:

-5 = 9+(c/4)

-5 -9 = (c/4)

-14 = c/4

c = -14*4

c = -56

Therefore, after solving the given equation for c, we know that the value of c is (A) -56.

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Answer: 325 adult tickets

Step-by-step explanation:

721 = (a+71) + a

721 = 2a + 71

2a = 650

a = 325

Lela is making peach pies. She uses 9 peaches for each pie. If she uses 18 peaches for 2 pies and 36 peaches for 4 pies, how many peaches will she need for 7 pies?

As, Lela is using 9 peaches for each pie.

Thus, she used 18 peaches for 2 pies, which is 2 times 9 and 36 peaches for 4 pies, which is 4 times 9. Therefore, to make 7 pies, she would need :

Peaches used for one pie = 9

=> Peaches used for 7 pies = 9 × 7

=> Peaches needed for 7 pies = 63

Hence, she will need 63 peaches to make 7 pies.

Answer:

in 40 minutes ... travelled 50km

Step-by-step explanation:

The relation represents y as a function of x as for each value of x there is a unique value of y.

A function y = f(x) is defined as a one to one relation between sets X and Y. The set X is called the domain while Y is called the range of f(x).

The given data is as follows,

A relation contains the points (1,2),(2,-1),(3,0),(4,1), and (5,-1).

Here x is the element of domain and y is of the range of the given relation.

Here, the values of y are distinct for different values of x.

Hence, the given relation represents y as a function of x  because for each value of x there is a single value of y.

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